Question

ABCD is a quadrilateral. AO and BO are the angle bisectors of angle A and B which meet at O. if /_ C = 70°, /_ D=50° , find the/_ AOB.​

Answer 1

Step-by-step explanation:

<A+<B+<C+<D = 360

LET ,

<A = <B = X

=> X+X+70°+50°=360°

=> 2X +120°=360°

=> 2X=240

=> X=240/2

=> X= 120

•°• <A = <B = 120°

<AO AND <BO BISECT <A AND <B

SO,

<A=120/2 = 60°

<B = 120/2 = 60°

THEREFORE,

<AOB + <OAB + <OBA = 180°

<AOB + <A + <B = 180°

<AOB + 120° = 180

<AOB = 180° - 120°

< AOB = 60°